Compound Inequality Word Problems

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities using the words 'and' or 'or'. It shows the range of values that satisfy all the inequalities.

Front

How do you represent a range of values in an inequality?

Back

A range of values can be represented using '≤' (less than or equal to) and '≥' (greater than or equal to) symbols, indicating the minimum and maximum values.

Front

If a person weighs 160 pounds, how do you calculate the range of food they can eat if it's between 3% and 7% of their body weight?

Back

Calculate 3% of 160 (4.8) and 7% of 160 (11.2). The range is 4.8 ≤ w ≤ 11.2.

Front

What does the inequality 5 ≤ m ≤ 10 represent in a word problem?

Back

It represents that the number of apples (m) you can buy is at least 5 and at most 10.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

Front

What does the solution 'All Real Numbers' mean in an inequality?

Back

It means that any real number satisfies the inequality.

Front

What is the significance of the 'and' in a compound inequality?

Back

The 'and' indicates that both conditions must be true at the same time for the solution to be valid.

Front

How do you solve the inequality -3x > -4 + 10?

Back

First, simplify to -3x > 6, then divide by -3 (remember to flip the inequality) to get x < -2.

Front

What does the inequality 90 ≤ x ≤ 120 represent in a word problem?

Back

It represents that the amount of food (x) a tiger can eat is between 90 and 120 pounds, inclusive.

Front

What is the first step in solving the inequality 2x - 1 < 5?

Back

Add 1 to both sides to isolate the term with x: 2x < 6.